Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26012041 | C2 | semidirect |
| 2. #26011881 | C2 | semidirect |
| 3. #26011850 | C2 | semidirect |
| 4. #26011703 | C2 | semidirect |
| 5. #26011630 | C2 | semidirect |
| 6. #26011625 | C2 | semidirect |
| 7. #26011548 | C2 | semidirect |
| 8. C2×#124×C173 | C2 | semidirect |
| 10. C2×#14583813 | C22 | semidirect |
| 12. #19149679 | C22 | semidirect |
| 13. #19149676 | C22 | semidirect |
| 18. C4×D692 | C22 | semidirect |
| 19. C4⋊#13063436 | C22 | semidirect |
| 20. #19149603 | C22 | semidirect |
| 23. #19149590 | C22 | semidirect |
| 120. C173 | #3213 | semidirect |
| 123. C2×#124 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012041 | 2 |
| #26011881 | 2 |
| #26011850 | 2 |
| #26011703 | 2 |
| #26011630 | 2 |
| #26011625 | 2 |
| #26011548 | 2 |
| C2×#124×C173 | 2 |
| #3213 | 173 |